Apparently, the Riemann matrix \(\Gamma =(\Gamma _{i,j})\)  is symmetric and has a
positive-definite imaginary part.
Let
\(\eta \in \mathbb {C},\,\,|\eta |<\textrm {min}\lbrace |E_0|^{-1},|E_{1}|^{-1},|E_{2}|^{-1},\cdots ,|E_{2n+1}|^{-1}\rbrace \) 
and abbreviate
\(\underline{E}=(E_{0},\cdots ,E_{2n+1}),\,\,\underline{E}^{-1}=(E_{0}^{-1},\cdots ,E_{2n+1}^{-1}).\) 
It turns out that [1]}
\(\left(\prod _{m=0}^{2n+1}(1-E_{m}\eta )\right)^{-1/2}=\sum _{k=0}^{\infty }\hat{c}_{k}(\underline{E})\eta ^{k},\) 
